Pileup involves the contamination of the energy distribution arising from the
primary collision of interest (leading vertex) by radiation from soft
collisions (pileup). We develop a new technique for removing this contamination
using machine learning and convolutional neural networks. The network takes as
input the energy distribution of charged leading vertex particles, charged
pileup particles, and all neutral particles and outputs the energy distribution
of particles coming from leading vertex alone. The PUMML algorithm performs
remarkably well at eliminating pileup distortion on a wide range of simple and
complex jet observables. We test the robustness of the algorithm in a number of
ways and discuss how the network can be trained directly on data.Comment: 20 pages, 8 figures, 2 tables. Updated to JHEP versio